Question 2
Archer Daniels Midland Company is considering buying a new farm that it plans to operate for 10 years. The farm will require an initial investment of $12.00 million. This investment will consist of $2.00 million for land and $10.00 million for trucks and other equipment. The land, all trucks, and all other equipment is expected to be sold at the end of 10 years at a price of $5.00 million, $2.12 million above book value. The farm is expected to produce revenue of $2.04 million each year, and annual cash flow from operations equals $1.92 million. The marginal tax rate is 35 percent, and the appropriate discount rate is 9 percent. Calculate the NPV of this investment. (Round intermediate calculations and final answer to 2 decimal places, e.g. 15.25.)
Question 3
Bell Mountain Vineyards is considering updating its current manual accounting system with a high-end electronic system. While the new accounting system would save the company money, the cost of the system continues to decline. The Bell Mountain’s opportunity cost of capital is 16.7 percent, and the costs and values of investments made at different times in the future are as follows:
Year Cost Value of Future Savings
(at time of purchase)
0 $5,000 $7,000
1 4,650 7,000
2 4,300 7,000
3 3,950 7,000
4 3,600 7,000
5 3,250 7,000
Calculate the NPV of each choice. (Round answers to the nearest whole dollar, e.g. 5,275.)
The NPV of each choice is:
Question 4
Chip’s Home Brew Whiskey management forecasts that if the firm sells each bottle of Snake-Bite for $20, then the demand for the product will be 15,000 bottles per year, whereas sales will be 88 percent as high if the price is raised 8 percent. Chip’s variable cost per bottle is $10, and the total fixed cash cost for the year is $100,000. Depreciation and amortization charges are $20,000, and the firm has a 30 percent marginal tax rate. Management anticipates an increased working capital need of $3,000 for the year. What will be the effect of the price increase on the firm’s FCF for the year? (Round answers to nearest whole dollar, e.g. 5,275.)
Question 5
Capital Co. has a capital structure, based on current market values, that consists of 21 percent debt, 1 percent preferred stock, and 78 percent common stock. If the returns required by investors are 9 percent, 10 percent, and 16 percent for the debt, preferred stock, and common stock, respectively, what is Capital’s after-tax WACC? Assume that the firm’s marginal tax rate is 40 percent. (Round intermediate calculations to 4 decimal places, e.g. 1.2514 and final answer to 2 decimal places, e.g. 15.25%.)
Question 2
To calculate the NPV of the investment, we need to find the present value of cash inflows minus the present value of cash outflows.
Cash inflows:
Initial investment: $12,000,000
Annual cash flow from operations x 10 years: $1,920,000 x 10 = $19,200,000
Sale at the end of 10 years: $5,000,000 + $2,120,000 = $7,120,000
Total cash inflows: $12,000,000 + $19,200,000 + $7,120,000 = $38,320,000
Cash outflows:
Initial investment: $12,000,000
Present value of cash inflows:
PV = CF / (1 + r)^n
PV = $38,320,000 / (1 + 0.09)^10
PV = $38,320,000 / 2.3674
PV = $16,195,016.87
NPV = present value of cash inflows - initial investment
NPV = $16,195,016.87 - $12,000,000
NPV = $4,195,016.87
The NPV of this investment is $4,195,016.87.
Question 3
To calculate the NPV of each choice, we need to find the present value of the future savings minus the cost of each investment:
Year 0:
NPV = ($7,000 - $5,000) / (1 + 0.167)^0 = $2,000
Year 1:
NPV = ($7,000 - $4,650) / (1 + 0.167)^1 = $2,350 / 1.167 = $2,014
Year 2:
NPV = ($7,000 - $4,300) / (1 + 0.167)^2 = $2,700 / 1.361 = $1,982
Year 3:
NPV = ($7,000 - $3,950) / (1 + 0.167)^3 = $3,050 / 1.588 = $1,920
Year 4:
NPV = ($7,000 - $3,600) / (1 + 0.167)^4 = $3,400 / 1.854 = $1,832
Year 5:
NPV = ($7,000 - $3,250) / (1 + 0.167)^5 = $3,750 / 2.166 = $1,731
The NPV of each choice is:
Year 0: $2,000
Year 1: $2,014
Year 2: $1,982
Year 3: $1,920
Year 4: $1,832
Year 5: $1,731
Question 4
First, we need to find the change in the number of bottles sold and the change in revenue due to the price increase:
New price: $20 × 1.08 = $21.60
New demand: 15,000 × 0.88 = 13,200 bottles
Change in revenue: $21.60 × 13,200 - $20 × 15,000 = $284,640 - $300,000 = -$15,360
Next, we need to find the change in variable costs and calculate the change in operating income:
Change in variable costs: $10 × (13,200 - 15,000) = -$18,000
Change in operating income: -$15,360 + $18,000 = $2,640
Now we need to adjust the operating income for taxes and depreciation:
Depreciation and amortization charges: $20,000
Taxable income: $2,640 - $20,000 = -$17,360
Tax savings: -$17,360 × 0.3 = $5,208
Finally, we need to find the change in FCF:
Change in FCF = Change in operating income + Tax savings + Change in working capital
Change in FCF = $2,640 + $5,208 - $3,000 = $4,848
The effect of the price increase on the firm's FCF for the year is an increase of $4,848.
Question 5
To calculate the after-tax WACC, we can use the following formula:
WACC = (E/V) × Re + (P/V) × Rp + (D/V) × Rd × (1 - T)
Where E, P, and D are the market values of common stock, preferred stock, and debt, respectively, Re, Rp, and Rd are the returns required by investors for common stock, preferred stock, and debt, respectively, and V is the total market value of the capital structure (E + P + D).
E = 0.78, P = 0.01, and D = 0.21
Re = 0.16, Rp = 0.10, and Rd = 0.09
T = 0.40
WACC = (0.78 × 0.16) + (0.01 × 0.10) + (0.21 × 0.09 × 0.60)
WACC = 0.1248 + 0.0010 + 0.01134
WACC = 0.13714 or 13.71%
Capital's after-tax WACC is 13.71%.
Question 2:
To calculate the NPV of the investment, we need to find the present value of all cash flows.
1. Calculate the present value of the revenue:
PV of revenue = Revenue * (1 - Tax rate) / Discount rate
PV of revenue = $2.04 million * (1 - 0.35) / 0.09
PV of revenue = $1.326 million
2. Calculate the present value of the cash flow from operations:
PV of cash flow = Cash flow * (1 - Tax rate) / Discount rate
PV of cash flow = $1.92 million * (1 - 0.35) / 0.09
PV of cash flow = $1.248 million
3. Calculate the present value of the salvage value:
PV of salvage value = Salvage value / (1 + Discount rate)^n
PV of salvage value = $5.00 million / (1 + 0.09)^10
PV of salvage value = $2.184 million
4. Calculate the NPV:
NPV = PV of revenue + PV of cash flow - Initial investment + PV of salvage value
NPV = $1.326 million + $1.248 million - $12.00 million + $2.184 million
NPV = -$7.242 million
The NPV of this investment is -$7.242 million.
Question 3:
To calculate the NPV of each choice, we need to find the present value of future savings for each year.
Year 0:
NPV0 = Value of Future Savings - Cost
NPV0 = $7,000 - $5,000
NPV0 = $2,000
Year 1:
NPV1 = Value of Future Savings - Cost
NPV1 = $7,000 - $4,650
NPV1 = $2,350
Year 2:
NPV2 = Value of Future Savings - Cost
NPV2 = $7,000 - $4,300
NPV2 = $2,700
Year 3:
NPV3 = Value of Future Savings - Cost
NPV3 = $7,000 - $3,950
NPV3 = $3,050
Year 4:
NPV4 = Value of Future Savings - Cost
NPV4 = $7,000 - $3,600
NPV4 = $3,400
Year 5:
NPV5 = Value of Future Savings - Cost
NPV5 = $7,000 - $3,250
NPV5 = $3,750
The NPV of each choice is:
Choice 0: $2,000
Choice 1: $2,350
Choice 2: $2,700
Choice 3: $3,050
Choice 4: $3,400
Choice 5: $3,750
Question 4:
To calculate the effect of the price increase on the firm's FCF (Free Cash Flow) for the year, we need to calculate the change in total revenue and total variable costs.
1. Calculate the change in total revenue:
Change in revenue = demand * price increase percentage
Change in revenue = 15,000 bottles * 8% = 1,200 bottles
2. Calculate the change in total variable costs:
Change in variable costs = demand * (price increase percentage) * variable cost per bottle
Change in variable costs = 15,000 bottles * 8% * $10 = $12,000
3. Calculate the change in FCF:
Change in FCF = Change in revenue - Change in variable costs - Increase in working capital
Change in FCF = 1,200 bottles * $20 - $12,000 - $3,000
Change in FCF = $24,000 - $12,000 - $3,000
Change in FCF = $9,000
The effect of the price increase on the firm's FCF for the year will be an increase of $9,000.
Question 5:
To calculate the after-tax WACC (Weighted Average Cost of Capital) of Capital Co., we need to calculate the weighted average of the required returns for each component of the capital structure.
1. Calculate the weight for each component:
Weight of debt = 21%
Weight of preferred stock = 1%
Weight of common stock = 78%
2. Calculate the after-tax required return for debt:
After-tax required return for debt = Required return for debt * (1 - Tax rate)
After-tax required return for debt = 9% * (1 - 0.4)
After-tax required return for debt = 5.4%
3. Calculate the weighted average cost of capital:
After-tax WACC = (Weight of debt * After-tax required return for debt) + (Weight of preferred stock * Required return for preferred stock) + (Weight of common stock * Required return for common stock)
After-tax WACC = (21% * 5.4%) + (1% * 10%) + (78% * 16%)
After-tax WACC = 1.134% + 0.1% + 12.48%
After-tax WACC = 13.714%
The after-tax WACC of Capital Co. is 13.714%.